Limits...
Modeling neutral evolution of Alu elements using a branching process.

Kimmel M, Mathaes M - BMC Genomics (2010)

Bottom Line: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes.A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, Rice University, Houston, TX 77005, USA. kimmel@rice.edu

ABSTRACT

Background: Alu elements occupy about eleven percent of the human genome and are still growing in copy numbers. Since Alu elements substantially impact the shape of our genome, there is a need for modeling the amplification, mutation and selection forces of these elements.

Methods: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes. From this model, we derive a limit frequency spectrum of the Alu element distribution, which serves as the theoretical, neutral frequency to which real Alu insertion data can be compared through statistical goodness of fit tests. Departures from the neutral frequency spectrum may indicate selection.

Results: A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.

Conclusions: This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

Show MeSH
Contour plot illustrating the influence of parameters b and p on Ψ1, based on Griffiths-Pakes process with linear-fractional distribution. Red: large Ψ1; blue: small Ψ1. Range of Ψ1-values, from 0 through 1.
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Figure 6: Contour plot illustrating the influence of parameters b and p on Ψ1, based on Griffiths-Pakes process with linear-fractional distribution. Red: large Ψ1; blue: small Ψ1. Range of Ψ1-values, from 0 through 1.

Mentions: The infinite sums in the numerator and denominator are numerically computed. A program was written in R-language to compute the Ψj. Since Alu sequence data in Table 1 suggest a high value for Ψ1, we verify that the theoretical Ψ1 attains such values for any choices of parameters b, p, and μ. For fixed μ = 10-6, we established a grid of b and p from 0 to 1 in steps of 0.01. Figure 6 shows that Ψ1 can assume any value between 0 and 1, and that high values of Ψ1 occur for a combination of low values of b and high values of p.


Modeling neutral evolution of Alu elements using a branching process.

Kimmel M, Mathaes M - BMC Genomics (2010)

Contour plot illustrating the influence of parameters b and p on Ψ1, based on Griffiths-Pakes process with linear-fractional distribution. Red: large Ψ1; blue: small Ψ1. Range of Ψ1-values, from 0 through 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2822525&req=5

Figure 6: Contour plot illustrating the influence of parameters b and p on Ψ1, based on Griffiths-Pakes process with linear-fractional distribution. Red: large Ψ1; blue: small Ψ1. Range of Ψ1-values, from 0 through 1.
Mentions: The infinite sums in the numerator and denominator are numerically computed. A program was written in R-language to compute the Ψj. Since Alu sequence data in Table 1 suggest a high value for Ψ1, we verify that the theoretical Ψ1 attains such values for any choices of parameters b, p, and μ. For fixed μ = 10-6, we established a grid of b and p from 0 to 1 in steps of 0.01. Figure 6 shows that Ψ1 can assume any value between 0 and 1, and that high values of Ψ1 occur for a combination of low values of b and high values of p.

Bottom Line: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes.A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, Rice University, Houston, TX 77005, USA. kimmel@rice.edu

ABSTRACT

Background: Alu elements occupy about eleven percent of the human genome and are still growing in copy numbers. Since Alu elements substantially impact the shape of our genome, there is a need for modeling the amplification, mutation and selection forces of these elements.

Methods: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes. From this model, we derive a limit frequency spectrum of the Alu element distribution, which serves as the theoretical, neutral frequency to which real Alu insertion data can be compared through statistical goodness of fit tests. Departures from the neutral frequency spectrum may indicate selection.

Results: A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.

Conclusions: This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

Show MeSH